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razmtaz
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Homework Statement
if m, n are distinct odd primes, show that the set of units mod mn has no primitive root.
Homework Equations
[ hint: phi(mn) = (m-1)(n-1) so we can show for a, a unit mod mn, a((m-1)(n-1))/2 = 1
]
and a [itex]\equiv[/itex] b mod mn iff a[itex]\equiv[/itex] b mod m and a [itex]\equiv[/itex] b mod n
The Attempt at a Solution
Not sure where to start with this one. I am thinking its fairly fundamental to understanding congruence classes and such, but the hint is throwing me off. In particular how can I show that for a unit a, a((m-1)(n-1))/2 = 1 ?after that, I know that a is a primitive root mod m if ord(a) = phi(m). this would give a(m-1)(n-1) = 1. If I could get to the point in the hint, then I would have a contradiction here and could conclude that there is no primitive root mod mn. So (assuming this is the correct approach) how can I get to a((m-1)(n-1))/2 = 1?
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